Seismic waves generated by rockfalls contain valuable information on the properties of these events. However, as rockfalls mainly occur in mountainous regions, the generated seismic waves can be affected by strong surface topography variations. We present a methodology for investigating the influence of topography using a Spectral-Element-based simulation of 3D wave propagation in various geological media. This methodology is applied here to Dolomieu crater on the Piton de la Fournaise volcano, Reunion Island, but it can be used for other sites, taking into account local topography and medium properties. The complexity of wave fields generated by single-point forces is analyzed for different velocity models and topographies. Ground-motion amplification is studied relative to flat reference models, showing that Peak Ground Velocity (PGV) and total kinetic energy can be amplified by factors of up to 10 and 20, respectively. Simulations with Dolomieu-like crater shapes suggest that curvature variations are more influential than depth variations. Topographic effects on seismic signals from rockfalls at Dolomieu crater are revealed by inter-station spectral ratios. Results suggest that propagation along the topography rather than source direction dominates the spectral ratios and that resulting radiation patterns can be neglected. The seismic signature of single rockfall impacts is studied. Using Hertz contact theory, impact force and duration are estimated and then used to scale simulations, achieving order-of-magnitude agreement with observed signal amplitudes and frequency thresholds. Our study shows that combining Hertz theory with high-frequency seismic wave simulations on real topography improves the quantitative analysis of rockfall seismic signals.

Rockfalls generate seismic signals that can be used to detect and monitor rockfall activity. Event locations can be estimated on the basis of arrival times, amplitudes or polarization of these seismic signals. However, surface topography variations can significantly influence seismic wave propagation and hence compromise results. Here, we specifically use the signature of topography on the seismic signal to better constrain the source location. Seismic impulse responses are predicted using Spectral Element based simulation of 3D wave propagation in realistic geological media. Subsequently, rockfalls are located by minimizing the misfit between simulated and observed inter-station energy ratios. The method is tested on rockfalls at Dolomieu crater, Piton de la Fournaise volcano, Reunion Island. Both single boulder impacts and distributed granular flows are successfully located, tracking the complete rockfall trajectories by analyzing the signals in sliding time windows. Results from the highest frequency band (here 13-17\,Hz) yield the best spatial resolution, making it possible to distinguish detachment positions less than 100\,m apart. By taking into account surface topography, both vertical and horizontal signal components can be used. Limitations and the noise robustness of the location method are assessed using synthetic signals. Precise representation of the topography controls the location resolution, which is not significantly affected by the assumed impact direction. Tests on the network geometry reveal best resolution when the seismometers triangulate the source. We conclude that this method can improve the monitoring of rockfall activity in real time once a simulated database for the region of interest is created.

The variations of elastic parameters and attenuation of rock under deformation are of great importance for a number of geophysical problems. Here, we estimate elastic parameters and their evolutions during laboratory rock deformation experiments, while developing a Monte-Carlo full-waveform fitting method. The transducer-transducer one-source one-station active seismic data of dry and water-saturated samples are obtained from Zaima and Katayama (2018, https://doi.org/10.1029/2018JB016377). The synthetic seismic data are modeled using the spectral element method. We first performed a trial-and-error estimate of the boundary conditions in order to suppress its influence on waveform matching. The synthetic seismic data are generated using equivalent homogeneous models with different combinations of elastic and anelastic parameters. We then compared the synthetics with the laboratory experimental data. Based on these comparisons, we obtain the time-lapse variations of seismic velocities and attenuation of rock samples during deformation, which are then interpreted as crack development. Our simultaneous estimation of elastic and anelastic parameters allowed us to detail the dynamics prior to the rock failure.

Seismic anisotropy in the Earth’s mantle inferred from seismic observations is usually interpreted either in terms of intrinsic anisotropy due to Crystallographic Preferred Orientation (CPO) of minerals, or extrinsic anisotropy due to rock-scale Shape Preferred Orientation (SPO). The coexistence of both contributions misconstrues the origins of seismic anisotropy observed in seismic tomography models. It is thus essential to discriminate CPO from SPO. Homogenization/upscaling theory provides means to achieve this goal. This theory enables to compute the effective elastic properties of a heterogeneous medium, as seen by long-period waves. In this work, we investigate the effects of upscaling an intrinsically anisotropic and highly heterogeneous Earth’s mantle. We show analytically in 1-D that the full effective radial anisotropy ξ * is approximately the product of the effective intrinsic radial anisotropy ξ * CPO and the extrinsic radial anisotropy ξ * SPO : ξ * ≈ ξ * CPO x ξ * SPO. This law is verified numerically in the case of a 2-D marble cake model of the mantle with a binary composition, and in the presence of CPO obtained from a micro-mechanical model of olivine deformation. We compute the long-wavelength effective equivalent of this mantle model using the 3-D non-periodic elastic homogenization technique. Our numerical findings predict that for wavelenghts smaller than the scale of deformation patterns, tomography may overestimate the true anisotropy (i.e. intrinsic anisotropy due to CPO) due to significant SPO-induced extrinsic anisotropy. However, at wavelenghts larger than deformation patterns, intrinsic anisotropy is always underestimated in tomographic models due to the spatial averaging of the preferred orientation of anisotropic minerals. Thus, we show that it is imperative to homogenize a CPO evolution model first before drawing comparisons with tomographic models. As a demonstration, we use our composite law with a homogenized CPO model of a plate-driven flow underneath a mid-ocean ridge, to estimate the SPO contibution to an existing tomographic model of radial anisotropy.

We quantitatively evaluate transducer-transducer one-source one-station active seismic waveform data, in order to monitor time-lapse changes of elastic and anelastic structure during deformation experiments in laboratory. The experiment data of dry and water-saturated sample are provided by Zaima and Katayama (2018, https://doi.org/10.1029/2018JB016377). A transducer receiver, at the mid-point of cylindrical rock sample, is located on the antipodal position of the transducer source, emitting compressional and shear waves. Due to the extremely underdetermined nature of inverse problem, we limit the number of unknowns to be four: global P- and S- wave velocities and their corresponding anelastic attenuation factors, which can represent the micro-cracks nucleation during the loading and before the appearance of the largest crack that causes the fracture. We first performed a trial-and-error search for a realistic boundary condition in three-dimensional seismic waveform modeling using spectral-element method, in order to fit the synthetic data with the observed waveforms. We then generated synthetic data for 6000 combinations of elastic and anelastic parameters, in order to conduct Monte-Carlo waveform inversion based on the cost functions using waveform misfit and zero-lag cross-correlation. We obtained the time-lapse changes in velocity and attenuation during the deformation, which are then linked to crack development. Compared with the wet experiment, the dry experiment has a larger change in both the velocity and attenuation. However, regardless of the configuration, global seismic wave speeds rise first and then decrease during the experiments. The quality factor shows roughly the same trend.